The accuracy of autocalibrating parallel imaging reconstructions such as GRAPPA has recently been shown to improve through the use of a 2D convolution kernel; however, the extension to a 2D kernel significantly increases computation time. We demonstrate that autocalibrating reconstruction methods can be separated into two processing steps and that each step can be independently optimized in terms of computational efficiency. The most computationally efficient means of obtaining the accuracy of a 2D k-space kernel is to find the kernel weights in k-space and then apply the weights in either image space or hybrid space, depending on the specific application.